The Johnson graph \(J(p,k)\)  is the graph whose vertices are the \(k-\) element subsets of a \(p-\) element set. Two vertices are adjacent when the intersection of two vertices (subsets) contains \((k - 1)\)  elements. Properties of \(J(p,k)\)  include the following, with the eigenvalues from [1]}.
\(n = {p \atopwithdelims ()k} \mbox{ ; } 2m = k(p - k){p \atopwithdelims ()k} \mbox{ ; } p \ge 2k \mbox{ and } \omega = 1 - \frac{\mu _1}{\mu _n} = p-k+1.\) 
